The Grade 4 Math session on Thursday focused on the Module 5: Fraction Equivalence, Ordering and Operations. Number bonds, tape diagrams, and area models were used consistently throughout the module to strengthen conceptual understanding and develop confidence when working with fractions. This “fractional” confidence allows students to transition to concepts/problems of higher complexity, which was demonstrated as we went through the lessons.
Students start their fraction work off with experiencing problems that involve decomposing fractions using number bonds, similar to the work they did with number bonds and whole numbers in the earlier grades. How many ways can you represent 5/6 as an addition problem? When answering this problem, students encounter how to express a non-unit fraction as a whole number times a unit fraction. The work here is extended to fractions that are greater than 1, such as decomposing 7/4 = 4/4 + 3/4 .
Fraction equivalence is explored using tape diagrams (paper folding) and area models. Participants look at an application problem from lesson 5:
A loaf of bread was cut into six equal slices. Each of the slices was cut in half to make thinner slices for sandwiches. Mr. Beach used four slices. His daughter said, “Wow, you used 2/6 of the loaf.” His son said, “No, you used 4/12.” Work with a partner to explain who was correct using a tape diagram.
This problem pulls in all content discussed so far, and solving the problem does not require a fractional algorithm. Fraction equivalence is extended to fraction comparison. Students combine knowledge of benchmark fractions with fraction equivalence to handle comparisons that involve fractions with common numerators, fractions with denominators of related units. The final goal is comparing fractions with denominators of unrelated units. Topic D shows once again the link of the work done previously with decomposition and composition to the addition and subtraction of fractions with common denominators. A new visual is added here, the number line with arrows.
Topics E and F add a layer of complexity to what has been learned by extending fractional equivalence and operations to fractions greater than 1. Based on their knowledge, students devise their own strategy for handling problems like 3 3/5 – 4/5. Some might decompose the 4/5 to be 3/5 and 1/5, and then solve the simpler problem of 3 1/5, which is 2 4/5. Others might decompose the 3 as 2 5/5 and now look at the problem 2 8/5 – 4/5, which is 2 4/5. Students practice converting between improper fractions and mixed numbers based on the context of the problem. Never is the traditional algorithm of how to convert a mixed number into an improper fraction discussed. The module shows that the algorithm is not necessary. The module ends with a re-visit to repeated addition of fractions as multiplication and shows the connection to the distributive property when solving problems like 2 x 3 1/5. Visuals are used again here to help make the connection.
The remainder of the session presented educators with a plan on how to make choices with implementing the lessons within the given time frame that remains between now and the assessment. Pacing is a huge area of concern and many teachers are behind the timeline. So how do we adapt the lessons to support successful pacing while bridging gaps in prior knowledge, but not sacrifice the rigor?
A planning protocol was introduced that encourages teachers to look at the lessons further out, not day to day. Reading the module overview and studying the module assessments is the place to start in order to keep the purpose, sequence and delivery fresh in the mind. Next, teachers should read through the lesson and ask what major concept is necessary to successfully complete the exit ticket. Pay attention to the subsequent lesson and examine the exit ticket there. What is the relationship between the two exit tickets and what will be the impact of what gets cut out of the lesson to those two tickets? Teachers also always need to consider the needs of specific students in their classroom.